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    $\begingroup$ 1)- Singularity points are points where particles are in same state. In CM, that means being at same position in configuration space, for QM it may mean same position in phase space. 3)- Because electrons and other particles are excitations of fields in 3D which is our physical world. Excitations in 2D gives anyons. If our world was 2D, anyons could have been the fundamental particles instead of electrons and quarks. Please add to this as its not a complete answer. $\endgroup$ Commented May 21 at 19:04
  • $\begingroup$ Please narrow this down into a single question. $\endgroup$ Commented May 23 at 12:03